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Homework Help: A_i,j - A_j,i is a tensor

  1. Sep 24, 2006 #1
    prove that for any vector


    the expression


    is a tensor, even under non-linear transformations. Similarly prove that for any antisymmetric tensor


    the expression


    is a tensor.


    What does the dots mean?
    For example between i and j in i.j ?
    Last edited: Sep 24, 2006
  2. jcsd
  3. Sep 25, 2006 #2


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    Partial derivatives.

  4. Sep 25, 2006 #3
    I solved the problem except that about
    even under non-linear transformations.
    non-linear transformations from one set of coordinates to another?
    what changes if its non-linear transformations?
  5. Sep 25, 2006 #4
    Maybe non-linear means higher order terms in partials derivitives of the coordinates? They would cancel out in the examples given.
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